None.
Not applicable.
1. Field of the Invention
The preferred embodiments of the present invention relate generally to acoustic well logging. More particularly, the preferred embodiments relate generally to determining the acoustic velocity (slowness) and frequency dispersion of acoustic waves in an earth formation.
2. Background of the Invention
In the art of acoustic logging, the formation properties of interest are one or more of the compressional wave velocity, shear wave velocity and Stonley wave velocity. These acoustic velocities are indicative of the formation""s ability to hold and produce hydrocarbons. Operation of a typical acoustic tool may involve placing the tool in a well bore and firing one or more acoustic transmitters periodically, thus sending acoustic energy into the formation. The acoustic energy propagates along the formation wall in one or more propagation modes, e.g. compressional or shear wave modes. Receivers on the tool, spaced apart from the one or more transmitters and from each other, receive acoustic energy as the various waves move along the formation wall past the receivers. The amplitudes and arrival times of the various acoustic signals at the receivers are indicative of the velocity of the acoustic waves (or slowness, being the inverse of the velocity) within the formation.
Determining the acoustic velocity with early wireline acoustic logging tools involves an adaptation of data processing techniques used in seismic work. In particular, a method called semblance or coherence is used. U.S. Pat. No. 4,594,691 to Kimball, et al., (hereinafter the ""691 patent) is exemplary of related art wireline sonic acoustic logging tools that use this semblance/coherence measure for determining acoustic velocities within the formation. As exemplified in the ""691 patent, determining the acoustic velocity using a coherence calculation is merely a determination of the extent two or more received waveforms resemble one another. The semblance/coherence determination itself, however, is not at all concerned with the actual formation properties; rather, the power of the semblance/coherence measure is running the calculation on portions of each received waveform that should correspond based on an estimated slowness.
The semblance/coherence measure of the related art is run multiple times at multiple slowness values, and the slowness values where the waveforms show the best semblance/coherence are assumed to be the correct slowness values for the formation. However, some earth formations exhibit a property where the slowness of an acoustic wave is a function of its frequency. For example, a low frequency acoustic wave may have a slower acoustic velocity than a high frequency acoustic wave within the same formation. In some respects, anisotropic earth formations may exhibit this property. Moreover, some earth formations may actually skew the frequency of the acoustic signals as they propagate through the formation in addition to having different acoustic velocities for the various frequencies. Running a semblance/coherence measure to determine acoustic velocity in formations where frequency dispersion is present tends to mask the actual formation slowness in the plot because of the dispersion characteristics. FIG. 4 shows a related art time versus semblance plot from which the formation acoustic velocity may be, to some extent, determined. It is noted that in the related art time versus slowness plot of FIG. 4 (with the semblance value shown in isometric lines), it is not possible to determine the acoustic velocity as a function of frequency.
Thus, what is needed in the art is a way to determine the acoustic velocity (slowness) of acoustic waves in formations that exhibit frequency dispersion characteristics and/or propagate acoustic waves at different speeds depending on the frequency.
The problems noted above are solved in large part by a signal processing technique for acoustic logging devices. In particular, a downhole tool, whether a wireline device, a logging-while-drilling device or a measuring-while-drilling device, has a transmitter and a plurality of receivers spaced apart from the transmitter and from each other. Acoustic energy is launched into the formation from the transmitter, and the receivers detect the acoustic energy as it propagates along the borehole wall and in the formation, the receivers creating a plurality of time domain signals. The time domain signals are preferably Fourier transformed to create a frequency domain representation of each received signal.
Preferably, values from each frequency domain representation of the received signals at a selected frequency are used to create a correlation matrix. Eigenvectors and eigenvalues of the correlation matrix are determined with all the eigenvectors of the correlation matrix forming an orthogonal basis or space. Preferably, at least the one highest order eigenvector is removed to create a subspace, the at least one highest order eigenvector corresponding to the signal component in the overall received signals, as opposed to the noise. Thereafter, a plurality of test vectors arc applied to the subspace, with each test vector based on a different slowness estimation, to determine an objective function value indicative of the extent to which the test vector maps to or may be represented by the subspace. If the test vector maps to the subspace, the corresponding slowness value thus maps to the noise, indicating the estimated slowness is not correct. However, if the test vector does not significantly map to the subspace, this means that the test vector (and its estimated slowness) more closely represents the actual received signal. The objective function calculated for each test vector is preferably plotted in a slowness versus frequency plot. The process is repeated for multiple slowness values within a single correlation matrix, and for multiple correlation matrices across the frequency spectrum of the received signals. What is preferably produced is a slowness versus frequency graph which shows the slowness of the formation as a function of frequency, and thus shows the dispersion of the acoustic velocities within the formation.
The disclosed methods comprise a combination of features and advantages which enable them to overcome the deficiencies of the prior art devices. The various characteristics described above, as well as other features, will be readily apparent to those skilled in the art upon reading the following detailed description, and by referring to the accompanying drawings.